Consider the problem of performing Principle Components Analysis on the R dataset mtcars. (1) Should one perform a PCA on the scaled or unscaled data? Briefly justify your answer (2) Remove variable mpg from the dataset, and perform PCA on the rest of the data (without any data splitting). Compare the first eigenvector from each analysis, and briefly comment on the values contained in these vectors in terms of the role of each feature. What causes the difference, and why? (3) Based on the PCA of the scaled data, indicate which 5 variables seem to capture most of the information. Briefly justify your answer. (4) Fit a linear regression model using these 5 variables as predictors X, and mpg as the dependent variable Y. Are any of these variables significant predictors? Briefly explain why they are or are not.